I'm having trouble finding out how to solve this integral.

I know the correct answer is: 0.235619, but I want to know if my work is correct. So far, whenever I work it out, I don't get the right answer.

From the integral,

((1/2)(1-cos10x))^2

= (1/4) integral (1-cos10x)^2

=(1/4) integral (1-2cos10x * (cos10x)^2

=(1/4) integral 1-2cos10x * ((1/2)1+cos20x)

From there, I plugged in the numbers, but I'm not getting the correct answer. Help?